We now illustrate the behaviour of fGOT in different experimental challenges. We consider three sets of experiments. The first one deals with random unstructured graphs, which we represent by random Erdos-Renyi graphs. We demonstrate the benefits of using high-pass filters to define a graph distance, and show the speed advancement compared to the GOT algorithm presented in [1]}. In the second set of experiments, we consider highly structured graphs, represented by stochastic block models. We tackle the problem of matching communities and show the benefits of low-pass filters. We also highlight the superior performance of our novel stochastic algorithm. Finally, we evaluate our method on a benchmark graph classification task, and compare to several state-of-the-art methods for graph alignment. The hyperparameters for all experiments were set empirically (the exact values are in the Appendix).
